Finite Group Databasebeta

← #34060053

Subgroups — #34060053

Order 19072.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750646C211yesmaximal, characteristic
2#23750641C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5#23750177C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9C22⋊#11924753—21no—
10#18011966—21no—
11C4×#11924753C2212yes—
12#18011910C411yescharacteristic
13#18011909C411yescharacteristic
14#18011901—21no—
15#18011890C411yescharacteristic
16#18011888—21no—
17Q8×Dic149C2211yescharacteristic
18#18011876—21no—
19#18011876C2211yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22C22⋊Q8×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×Dic298—21no—
26C2×Dic298C2×C411yescharacteristic
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C411yescharacteristic
31#14558715—21no—
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36C22⋊Dic149—21no—
37C4×Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149C2×C411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149C2311yescharacteristic
43C2×Q8×C149C2×C411yescharacteristic
44C22×C4×C149C2×C411yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C22⋊C4×C149—21no—
48#11924753—42no—
49#11924753—42no—
50Dic298—22no—
51Dic298—42no—
52C2×Dic149—22no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—41no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C23×C149C22⋊C411yescharacteristic
61Q8×C149—22no—
62C2×C4×C149—22no—
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22×C411yescharacteristic
67C22×C149—21no—
68C22×C149—21no—
69C22×C149—21no—
70C22×C149C2×C22⋊C411yescharacteristic
71C4×C149—21no—
72C4×C149—41no—
73C4×C149—41no—
74C4×C149#13112yes—
75Dic149—21no—
76Dic149—21no—
77Dic149—21no—
78Dic149—41no—
79Dic149—41no—
80Dic149#13712yes—
81C2×C149—41no—
82C2×C149#40811yescharacteristic
83C2×C149#41911yescharacteristic
84C2×C149#42111yescharacteristic
85C149#149711yescharacteristic, complemented, Sylow
86#1497—1491nomaximal, Sylow
87#533—1491no—
88#432—1491no—
89#431—1491no—
90Q8⋊C8—1492no—
91Q8⋊C8—1492no—
92C4⋊Q8—1491no—
93C4⋊Q8—1491no—
94#125—2981no—
95C22⋊Q8—2981no—
96C22⋊Q8—1491no—
97C22⋊Q8#1059701011yescharacteristic
98C4×Q8—2981no—
99C4×Q8—1491no—
100C4×Q8—1491no—
101#117—2981no—
102C2×C42—1491no—
103C4⋊C8—2981no—
104C4⋊C8—1492no—
105C22⋊C8—2981no—
106C22⋊C8—2981no—
107#97—2981no—
108C4×C8—1492no—
109C2×Q8—2981no—
110C2×Q8—1491no—
111C2×Q8C2×#1059701011yescharacteristic
112C22×C4—1491no—
113C22×C4—1491no—
114C22×C4C2×#1059701011yescharacteristic
115C2×C8—2982no—
116C2×C8—2982no—
117C4⋊C4—21no—
118C4⋊C4—2981no—
119C4⋊C4—2981no—
120C4⋊C4—2981no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—1491no—
125C4⋊C4C2×#1059701011yescharacteristic
126C22⋊C4—21no—
127C22⋊C4—2981no—
128C42—2981no—
129C42—2981no—
130C42—1491no—
131C42—1491no—
132C42—1491no—
133C42—1491no—
134C23C22⋊#1059701011yescharacteristic
135Q8—22no—
136Q8—2982no—
137Q8—5962no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—2982no—
142C2×C4—2981no—
143C2×C4—2981no—
144C2×C4—5961no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4—1491no—
149C2×C4C22⋊#1059701011yescharacteristic
150C2×C4C22×#1059701011yescharacteristic
151C8—5962no—
152C8—5962no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#1059701011yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—2981no—
161C4—2981no—
162C4—2981no—
163C4—5961no—
164C4—5961no—
165C4—1492no—
166C4#1801199812yes—
167C2—41no—
168C2#2375059811yescharacteristic
169C2#2375061811yescharacteristic
170C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1497
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
85. C149#1497semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237506462
#237506412
#237504752
Q8⋊#119247532
#237501772
#1497149